Find the probability that a randomly selected point within the circle falls in the red shaded area (square)
Accepted Solution
A:
Answer:The probability that a randomly selected point within the falls in the shaded region is 0.6366Step-by-step explanation:Here in these cases probability, P=[tex]\frac{n(E)}{n(S)}[/tex]=[tex]\frac{required number of points}{Total number of points in sample space}[/tex]And collection of points is nothing but the area occupied by those pointsTherefore, P=[tex]\frac{Required Area }{TotalArea Of Sample Space}[/tex]Given: Radius, r=[tex]4[/tex] cm Side, s=[tex]4\sqrt{2}[/tex] cmIn this question, circle is the sample space,S, hence n(S)=area of the circle =π[tex]r^{2}[/tex] =16π cm² =50.265 cm²Let A be the event of selecting a random point within the circle such that it falls within the shaded regionSo, n(A)= area of the square =[tex]s^{2}[/tex] =32 cm²Therefore, the probability that a randomly selected point within the falls in the shaded region ,P(A)=[tex]\frac{Area Of The Square}{Area Of The Circle}[/tex]=[tex]\frac{32}{50.265} =0.6366[/tex]